Nearly Deconfined Spinon Excitations in the Square-Lattice Spin-1/2 Heisenberg Antiferromagnet

Abstract

We study the spin-excitation spectrum (dynamic structure factor) of the spin-1/2 square-lattice Heisenberg antiferromagnet and an extended model (the J−Q model) including four-spin interactions Q in addition to the Heisenberg exchange J . Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with quantum Monte Carlo simulations, we can treat the sharp (δ -function) contribution to the structure factor expected from spin-wave (magnon) excitations, in addition to resolving a continuum above the magnon energy. Spectra for the Heisenberg model are in excellent agreement with recent neutron-scattering experiments on Cu(DCOO)2·4D2O , where a broad spectral-weight continuum at wave vector q=(π,0) was interpreted as deconfined spinons, i.e., fractional excitations carrying half of the spin of a magnon. Our results at (π,0) show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at q=(π/2,π/2) (as also seen experimentally). We further investigate the reasons for the small magnon weight at (π,0) and the nature of the corresponding excitation by studying the evolution of the spectral functions in the J−Q model. Upon turning on the Q interaction, we observe a rapid reduction of the magnon weight to zero, well before the system undergoes a deconfined quantum phase transition into a nonmagnetic spontaneously dimerized state. Based on these results, we reinterpret the picture of deconfined spinons at (π,0) in the experiments as nearly deconfined spinons—a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile (π,0) -magnon pole in the Heisenberg model and its depletion in the J−Q model, we introduce an effective model of the excitations in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy to the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model can reproduce the reduction of magnon weight and lowered excitation energy at (π,0) in the Heisenberg model, as well as the energy maximum and smaller continuum at (π/2,π/2) . It can also account for the rapid loss of the (π,0) magnon with increasing Q and the remarkable persistence of a large magnon pole at q=(π/2,π/2) even at the deconfined critical point. The fragility of the magnons close to (π,0) in the Heisenberg model suggests that various interactions that likely are important in many materials—e.g., longer-range pair exchange, ring exchange, and spin-phonon interactions—may also destroy these magnons and lead to even stronger spinon signatures than in Cu(DCOO)2·4D2O .

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Plain Language Summary

Similar to how sound waves propagate through everyday materials, some materials can carry magnetic waves, which are collective excitations of electronic magnetic moments (or spins). These “spin waves” can be detected in neutron-scattering experiments. Theoretically, it is believed that the spin waves can sometimes split up (or fractionalize) into a different kind of excitation, called a spinon, which carries only half of the magnetic moment associated with a normal spin wave. Recent experiments have revealed anomalous spin-wave behavior in antiferromagnetic materials, where the electron spins are oriented antiparallel to their neighbors in the crystal lattice, like the colors of a checkerboard. This behavior suggests that spin waves propagating in certain directions are unstable and fractionalize into spinons. We demonstrate that this proposal is only partially correct.

Using a theoretical quantum spin model known to be an accurate representation of the experimental system and a novel computer-simulation method for extracting the dynamical signatures, we show that the anomalous spin waves are not quite broken up into spinons but exhibit a “mixed personality,” fluctuating between spinons and spin waves. However, by changing the parameters of the model, we can cause the spin wave to fully fractionalize. We also present a simplified theoretical picture in which the mechanism of fractionalization can be captured and understood.

Our achievement demonstrates that spinons are more common than previously thought. We argue that further signs of spin-wave fragility are present in existing neutron-scattering data, and we suggest experiments to test our proposed fractionalization mechanism.